Harmonic Series with Multinomial Coefficient $\left(\genfrac{}{}{0pt}{}{4n}{n,n,n,n}\right)$ and Central Binomial Coefficient $\left(\genfrac{}{}{0pt}{}{2n}{n}\right)$

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Attached 

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In this article, the author establishes several closed forms of harmonic series containing multinomial coefficients and central binomial coefficients. The article presents some valuable identities using the well-known method of "coefficient extraction." However, it is requested to provide the following information for better understanding of the readers.: 

1. Revise the abstract to reflect the entire concept of the article, including the methods used and an outline of the expected results. 

2. Probably the notation [x] is not defined anywhere. 

3. The classical hypergeometric series may converge for negative integer (i) a_j  or (ii) both a_j abd b_j with condition. so, why consider {a_j, b_j} both positive integer only? 

4.  Explain how the summation (at least few from the eight sums listed in the introduction) is obtained. If any computational software is used, please describe the process of using the software and provide a reference to it.

The article can be accepted after addressing the above comments. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. The abstract  of the paper should be rewritten. First it is too short and does not discover the content of the paper. Second it is not advisable to give formulas in the abstract, since in some indexing systems they are not readable.

2. The authors are advised to give more detailed information both about theoretical and practical applications of the considered problems and obtained results.

3. To cover all aspects of the considered problems the authors are advised to add the references below to the list of references and analyze them in the introduction:

Srivastava, H.M., Ansari, K.J., Özger, F., & Ödemiş Özger, Z. (2021). A link between approximation theory and summability methods via four-dimensional infinite matrices. Mathematics, 9(16), 1895.

Nadeem, M., Khan, W.A., Alzobydi, K.A.H., Ryoo, C.S., Shadab, M., Ali, R., & Arabia, S. (2023). Certain properties on bell-based apostol-type Frobenius-Genocchi polynomials and its applications. Advanced Mathematical Models & Applications, 8(1), 92-107.

 

 

Comments on the Quality of English Language

A minor language editing is advised.

Author Response

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Author Response File: Author Response.pdf